Does different method of integration yields different results?

In the link , I posted a question on mathematics stack exchange to remove my confusion about different methods and different results in integration

But it seems that I am having more confusion now, because in the answers , some experts believe both answers are right , but some other believe only one is right

I don't know how to convince myself for right answer

What should I do?

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    $\begingroup$ What about reading @projecilemotion's comment on main, posted 20 hours before this post on meta? It is concise, precise, and it completely solves your problem, going to the heart of the matter. What makes that you overlooked it? $\endgroup$ – Did Jul 24 '17 at 12:54
  • $\begingroup$ @Did Ksplit X says mine answer is wrong , this is why I am having confusion $\endgroup$ – Atul Mishra Jul 24 '17 at 13:12
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    $\begingroup$ Your answer is wrong. If you read the comment of projectilemotion carefully, he didn't say what you written down is correct. He is questioning whether you have a typo in writing down that answer. If there is indeed a typo, then both your and the book's answer is correct. If you insists you have written down what you get correctly, then you have make a sign error somewhere when you derive your result. $\endgroup$ – achille hui Jul 24 '17 at 15:42
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    $\begingroup$ So why do you accept an answer if it apparently did not solve your question? $\endgroup$ – miracle173 Jul 25 '17 at 23:47

You can proceed like this:

  1. Read in detail what the different users wrote and try to understand it. Do not just skim it. Read it carefully, using pen and paper if needed.

  2. Based on 1. ask for clarification in comments. There is nothing wrong with pointing out discrepancies between answer to the users that wrote them if you do so in a polite way.

  3. If all this fails, place a bounty on the question.

  • 2
    $\begingroup$ Hooray, quid. (Very good list). For the asker, I will also mention that "posting on meta a question I asked on the main math site, because I'm confused and hope someone will tell me what the correct answer is" is not on this list provided by quid. Try alternatives 1, 2. 3 that quid provides for you. $\endgroup$ – Namaste Jul 24 '17 at 19:20

Edit: Quid informed me in a comment that this question was posed before the answer was accepted.

You already accepted an answer. You didn't ask any question in a comment to this accepted answer. From this I would conclude that everything is fine: you got an answer and no open question are left.

  • Do not accept answers if they don't answer your question satisfactorily.
  • use comments to ask if anything is unclear in an answer
  • if there are comments to your question that answer your question you can ask the poster to post them as answers and elaborate it.

If you accept an answer too early this is not useful:

  • the answerer is not motivated to improve the answer
  • other users are not motivated to improve their already posted answers
  • other users are not motivated to post new answers

If you accepted an answer erroneously or come to the conclusion it was not a good choice you can consider to withdraw the acceptance.

  • 1
    $\begingroup$ It may be worth noting that the answer was accepted considerably (almost a full day) after this meta question was asked. In that sense while what you say can be true, it does not quite apply to the situation at hand (when the question was asked). Instead it seems that by now OP's problems are resolved (mostly by comments following the posting of the meta question), and thus they then accepted an answer. $\endgroup$ – quid Jul 26 '17 at 10:07
  • $\begingroup$ @quid I didn't check this but now I see. $\endgroup$ – miracle173 Jul 26 '17 at 15:05

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